A resonant photoelastic modulator (PEM) is an instrument that is used for modulating the polarization of a beam of light. A PEM employs the photoelastic effect as a principle of operation. The term “photoelastic effect” means that an optical element that is mechanically strained (deformed) exhibits birefringence that is proportional to the amount of strain induced into the element. Birefringence means that the refractive index of the element is different for different components of polarized light.
A PEM includes an optical element, such as fused silica, that has attached to it a piezoelectric transducer for vibrating the optical element at a fixed frequency, within, for example, the low-frequency, ultrasound range of about 20 kHz to 100 kHz. The mass of the element is compressed and extended as a result of the vibration.
The compression and extension of the optical element imparts oscillating birefringence characteristics to the optical element. The frequency of this oscillating birefringence is the resonant frequency of the optical element and is dependent on the size of the optical element, and on the velocity of the transducer-generated longitudinal vibration or acoustic wave through the optical element.
Retardation or retardance represents the integrated effect of birefringence acting along the path of electromagnetic radiation (a light beam) traversing the vibrating optical element. If the incident light beam is linearly polarized, two orthogonal components of the polarized light will exit the optical element with a phase difference, called the retardance. For a PEM, the retardation is a sinusoidal function of time. The amplitude of this phase difference is usually characterized as the retardance amplitude or retardation amplitude of the PEM.
In conventional PEMs, the value of the retardation amplitude is selectable by the user. Because resonant PEMs are typically driven at their resonant frequency, stress oscillations, which are induced by the transducer, can exhibit relatively large amplitudes. However, driving PEMs at their resonant frequency prevents the user from controlling the oscillation frequency.
Both the size and acoustic wave velocity of a PEM depend on the optical element's temperature. Consequently, the resonant frequency of a PEM will also depend on the device's temperature. In general, this temperature depends on two factors: (1) the ambient temperature, and (2) the amplitude of the stress oscillations in the optical element. At high stress amplitudes, the amount of acoustic (mechanical) energy absorbed in the optical element can become significant. As the absorbed acoustic energy is converted to heat within the mass of the element, significant temperature increases and corresponding shifts in the PEM's resonant frequency can occur.
PEMs having high retardance amplitudes are required, for example, in Fourier Transform spectral analysis (see, for instance, U.S. Pat. Nos. 4,905,169 and 5,208,651). In such applications, spectral resolution is proportional to the PEM's retardation amplitude, and useful spectral resolutions are achieved at high amplitudes, which cannot be reached by a conventional (single) PEM.
The most direct way of achieving these high-retardation amplitudes is to stack together several PEMs. In such an arrangement it is important that the sum or total of the retardation amplitudes of all of the PEMs matches the sum of the maximum retardation amplitudes of each of the PEMs in the stack.
Even if all the PEMs in a stack are driven at the same frequency, the total retardation amplitude of the stack may be less than the sum of the maximum retardation amplitudes of each of the PEMs in the stack. This is because even a relatively small spread in the resonant frequencies of the individual PEMs, which is fully consistent with manufacturing specifications, results in most of the PEMs not being driven exactly at resonance. As a result, the phases of the oscillations of the individual PEMs are not the same, even though the PEMs are driven at the same frequency, and, therefore, the total retardation amplitude is less than the sum of the individual amplitudes.
Furthermore, uneven heating of the individual PEMs when driven at high amplitudes may result in the individual resonant frequencies drifting by unequal amounts. Consequently, the phases of the individual PEM oscillations may further diverge as the driving amplitude is increased or as the system warms up. This may lead to a further decrease in the efficiency of the PEM stack.
The problem of drifting operating frequencies is not limited to stacked PEM arrangements. In a conventional single PEM system, even though the retardation amplitude can be adjusted at will (within the limits set by the maximum driving voltage provided by the electronic circuits), the system's operating frequency is determined by the PEM's resonant frequency and, as explained above, thus depends on both ambient temperature and the amplitude at which the PEM is driven. This results in an operating frequency that drifts with ambient temperature, as well as during warm-up and after changes in the set retardation amplitude. Such a situation may be undesirable in certain applications where the PEM's operating frequency, as well as its amplitude, must be kept constant.